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Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…

Machine Learning · Computer Science 2025-07-03 Di Zhang , Yihang Zhang

Adaptive gradient methods, such as Adam and LAMB, have demonstrated excellent performance in the training of large language models. Nevertheless, the need for adaptivity requires maintaining second-moment estimates of the per-parameter…

Computation and Language · Computer Science 2023-08-08 Yang Luo , Xiaozhe Ren , Zangwei Zheng , Zhuo Jiang , Xin Jiang , Yang You

We introduce AdamS, a simple yet effective alternative to Adam for large language model (LLM) pretraining and post-training. By leveraging a novel denominator, i.e., the root of weighted sum of squares of the momentum and the current…

Machine Learning · Computer Science 2025-05-23 Huishuai Zhang , Bohan Wang , Luoxin Chen

In the evolving landscape of natural language processing (NLP), fine-tuning pre-trained Large Language Models (LLMs) with first-order (FO) optimizers like SGD and Adam has become standard. Yet, as LLMs grow {in size}, the substantial memory…

Training and fine-tuning large language models (LLMs) come with challenges related to memory and computational requirements due to the increasing size of the model weights and the optimizer states. Various techniques have been developed to…

Machine Learning · Computer Science 2025-12-09 Yehonathan Refael , Jonathan Svirsky , Boris Shustin , Wasim Huleihel , Ofir Lindenbaum

Designing efficient optimizers for large language models (LLMs) with low-memory requirements and fast convergence is an important and challenging problem. This paper makes a step towards the systematic design of such optimizers through the…

Machine Learning · Computer Science 2025-02-21 Wenbo Gong , Meyer Scetbon , Chao Ma , Edward Meeds

Large language models (LLMs) demonstrate remarkable performance, and improving their pre-training process appears to be key to enhancing their capabilities further. Based on the documented success of Adam, learning rate decay, and weight…

Machine Learning · Computer Science 2025-01-22 Yizhou Liu , Ziming Liu , Jeff Gore

Lowering the memory requirement in full-parameter training on large models has become a hot research area. MeZO fine-tunes the large language models (LLMs) by just forward passes in a zeroth-order SGD optimizer (ZO-SGD), demonstrating…

Machine Learning · Computer Science 2023-12-27 Shuoran Jiang , Qingcai Chen , Youchen Pan , Yang Xiang , Yukang Lin , Xiangping Wu , Chuanyi Liu , Xiaobao Song

Low-rank training has emerged as a promising approach for reducing memory usage in training Large Language Models (LLMs). Previous methods either rely on decomposing weight matrices (e.g., LoRA), or seek to decompose gradient matrices…

Machine Learning · Computer Science 2025-11-18 Xi Chen , Kaituo Feng , Changsheng Li , Xunhao Lai , Xiangyu Yue , Ye Yuan , Guoren Wang

The impressive performance of large language models (LLMs) arises from their massive scale and heterogeneous module composition. However, this structural heterogeneity introduces additional optimization challenges. While adaptive optimizers…

Machine Learning · Computer Science 2026-05-08 Ziqing Wen , Zhouyang Liu , Jiahuan Wang , Ping Luo , Li Shen , Dongsheng Li , Tao Sun

Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that…

Machine Learning · Computer Science 2025-03-19 Dayal Singh Kalra , John Kirchenbauer , Maissam Barkeshli , Tom Goldstein

We investigate the effectiveness of adaptive zeroth-order (ZO) optimization for memory-constrained fine-tuning of large language models (LLMs). Contrary to prior claims, we show that adaptive ZO methods such as ZO-Adam offer no convergence…

Machine Learning · Computer Science 2026-05-06 Hassan Dbouk , Nidham Gazagnadou , Matthias Reisser , Christos Louizos

Training large language models (LLMs) poses challenges due to their massive scale and heterogeneous architectures. While adaptive optimizers like AdamW help address gradient variations, they still struggle with efficient and effective…

Machine Learning · Computer Science 2025-06-03 Siyuan Li , Juanxi Tian , Zedong Wang , Xin Jin , Zicheng Liu , Wentao Zhang , Dan Xu

Training Large Language Models (LLMs) is highly memory-intensive due to optimizer state overhead. The FRUGAL framework mitigates this with gradient splitting, but its static hyperparameters -- the subspace ratio ($\rho$) and update…

Machine Learning · Computer Science 2026-04-30 Quang-Hung Bui , Anh Son Ta

Training LLMs presents significant memory challenges due to growing size of data, weights, and optimizer states. Techniques such as data and model parallelism, gradient checkpointing, and offloading strategies address this issue but are…

Machine Learning · Computer Science 2024-10-22 Arijit Das

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence…

Machine Learning · Computer Science 2026-05-12 Kristi Topollai , Anna Choromanska

Large language model (LLM) unlearning aims to surgically remove the influence of undesired data or knowledge from an existing model while preserving its utility on unrelated tasks. This paradigm has shown promise in addressing privacy and…

Machine Learning · Computer Science 2026-04-21 Yicheng Lang , Yihua Zhang , Chongyu Fan , Changsheng Wang , Jinghan Jia , Sijia Liu

Define an optimizer as having memory $k$ if it stores $k$ dynamically changing vectors in the parameter space. Classical SGD has memory $0$, momentum SGD optimizer has $1$ and Adam optimizer has $2$. We address the following questions: How…

Machine Learning · Computer Science 2024-02-26 Balázs Szegedy , Domonkos Czifra , Péter Kőrösi-Szabó

Adaptive gradient-based optimizers such as Adagrad and Adam are crucial for achieving state-of-the-art performance in machine translation and language modeling. However, these methods maintain second-order statistics for each parameter,…

Machine Learning · Computer Science 2019-09-13 Rohan Anil , Vineet Gupta , Tomer Koren , Yoram Singer

Training with larger mini-batches improves the convergence rate and can yield superior performance. However, training with large mini-batches becomes prohibitive for Large Language Models (LLMs), due to the large GPU memory requirement. To…

Machine Learning · Computer Science 2025-05-29 Dang Nguyen , Wenhan Yang , Rathul Anand , Yu Yang , Baharan Mirzasoleiman